1. Field of the Invention
The present invention concerns a method of migrating geophysical attributes of a medium and more particularly of a given area of said medium.
2. Description of the Related Art
Reflection seismic prospecting is a standard method used, in particular in petroleum exploration, to obtain a seismic image of the medium to be explored. In this method, using appropriate energy sources called emitters, acoustic waves are emitted that propagate in the medium to be explored and are reflected at the various reflectors or horizons that it contains. The reflected waves are recorded as a function of time by appropriate receivers disposed on the surface of the medium.
The records or traces are then grouped in accordance with a criterion determined in accordance with objectives to be achieved and constitute trace gathers. The common mid-point (CMP) trace gather groups the series of traces that are assigned to points midway along the straight line segments linking the emitter-receiver pairs used to obtain said traces.
Seismic processing derives from said trace gathers a seismic image in the vertical plane through the set of mid-points. If it is assumed that the medium is homogeneous and isotropic, with plane and parallel layers, the reflections of the waves at the various reflectors observed on a common mid-point trace gather are theoretically aligned with hyperbolas called indicators centred on a vertical line through the mid-point. To stack the traces of each gather, said traces are corrected dynamically using a velocity field or law V(t). One way to obtain this velocity field is to carry out individual velocity analyses on a limited number of common mid-point trace gathers and then to interpolate the results of such analyses, in time, on the one hand, for each of the analyses, and in space, along the abscissa axis, on the other hand.
The standard velocity analysis consists in successively applying constant velocities to the CMP trace gathers for the selected mid-points and then stacking the dynamically corrected traces for each of the velocities used and manually selecting the velocities yielding an energy maximum of the stack trace.
In an article entitled "Normal Moveout Revisited: Inhomogeneous media and curved interfaces" published in GEOPHYSICS, Volume 53, No 2, February 1988, pages 143 through 157, Eric de Bazelaire has developed another velocity analysis method used to obtain improved stack sections known as "POLYSTACKS". Briefly, the POLYSTACK method consists in scanning all the traces of a same CMP trace gather and applying a static correction to all the traces in accordance with a family of hyperbolas independent of time and different from one stack trace to another, in order to produce "BAP", each trace of which is a stack of traces from the CMP gather corrected in this way.
Another method, more sophisticated than the "POLYSTACK" method, is described in patent application FR-A-2 726 091. This other method, known as the DELTA STACK method yields, as previously, a refined velocity field of better resolution and an improved stack section, using "BAP" of the POLYSTACK type but of smaller size.
The POLYSTACK and DELTA STACK methods both have the peculiarity of including and/or of making more accessible the geophysical attributes of the area of the medium explored, including the amplitude and velocity attributes, of course.
The stack section obtained by the various methods outlined above includes a number of anomalies (diffraction hyperbola, poor location of dipping events, etc) that have to be corrected.
When the area of the medium to be explored is isotropic, homogeneous, with plane and parallel layers, the slice or interval velocities can easily be calculated using the DIX formula well known to the skilled person.
In the case of an area comprising dipping reflectors, it is necessary to apply a correction before migration known as DMO (DIP MOVE OUT).
The stack section can be migrated in time or in depth according to the aims to be achieved, with the facility for switching from time migration to depth migration and vice versa. This is well known to the skilled person and will not be described in detail, the effect of the migration being to move the seismic event or events appearing on the stack section back straight up of their geological position.
To migrate a seismic signal it is necessary to know the distribution of velocities in the subsurface which, in geophysical terms, amounts to knowing the interval velocity field in the migrated position.
In fact, the interval velocity field is an unknown, regardless of the migration technique used: wave equation or ray tracing; it is replaced by a velocity distribution law obtained from the stack or from any other form of modelling. Any error in respect of this velocity field introduces a skew into the results of the amplitude migration in particular.